Description
Book SynopsisNow revised and updated, this brisk introduction to functional analysis is intended for advanced undergraduate students, typically final year, who have had some background in real analysis. The author's aim is not just to cover the standard material in a standard way, but to present results of application in contemporary mathematics and to show the relevance of functional analysis to other areas. Unusual topics covered include the geometry of finite-dimensional spaces, invariant subspaces, fixed-point theorems, and the Bishop-Phelps theorem. An outstanding feature is the large number of exercises, some straightforward, some challenging, none uninteresting.
Trade Review' … a well-written concise introduction to functional analysis.' European Mathematical Society
'Bollobás writes with clarity and has clearly thought about the needs of his readers. First-time students of functional analysis will thank him for his willingness to remind them about notation and to repeat definitions that he has not used for a while. Bollobás has written a fine book. it is an excellent introduction to functional analysis that will be invaluable to advanced undergraduate students (and their lectures). Steve Abbott, The Mathematical Gazette
Table of ContentsPreface; 1. Basic inequalities; 2. Normed spaces and bounded linear operators; 3. Linear functional and the Hahn-Banach theorem; 4. Finite-dimensional normed spaces; 5. The Baire category theorem and the closed-graph theorem; 6. Continuous functions on compact spaces and the Stone-Weierstrass theorem; 7. The contraction-mapping theorem; 8. Weak topologies and duality; 9. Euclidean spaces and Hilbert spaces; 10. Orthonormal systems; 11. Adjoint operators; 12. The algebra of bounded linear operators; 13. Compact operators on Banach spaces; 14. Compact normal operators; 15. Fixed-point theorems; 16. Invariant subspaces; Index of notation; Index of terms.
